All Questions
31
questions
0
votes
3
answers
222
views
2+1-dimensional $SU(N)$ Yang-Mills Theory
In recent years, there has been significant progress and growing interest in conducting quantum simulations of field theories using quantum devices. This typically involves formulating a Hamiltonian ...
- 857
1
vote
1
answer
53
views
Reference request: scalar $O(N)$ gauge theory
I am interested in scalar $O(N)$ gauge theory and what you can do with it. Is there a standard reference section in a textbook/monograph/paper/whatever that has a decent overview?
Wikipedia has a ...
2
votes
1
answer
75
views
Why the expectation value of three currents is important in the anomaly?
I am studying the anomalies chapter (Chapter 30) of Schwartz's [Quantum Field Theory and the Standard Model]. I want to ask why the expectation of three currents, $\langle J^\mu J^\nu J^\rho \rangle$, ...
- 79
0
votes
0
answers
98
views
Why is the source of the EM Field in QED the probability current and not the electric current?
I have some problems understanding the interaction term in the QED Lagrangian. If we take
$$
\mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \bar \psi (\gamma^\mu\partial_\mu-m)\psi+\bar \psi \gamma^\...
- 29
1
vote
0
answers
46
views
Group factors in scalar-gauge box diagram
So, I'm currently writing my Thesis, which involves one-loop beta functions of a general $SU(N)$ for scalars and fermions fields, Yukawa coupling and one scalar self-coupling.
To this moment I was ...
- 21
8
votes
1
answer
279
views
Assumptions behind the Quantum Master Equation derived using Batalin-Vilkovisky Formalism
Is there any underlying assumption(s) behind the Batalin-Vilkovisky Quantum Master Equation:
$$\frac{1}{2}(S,S) = i\hbar\Delta(S)~?$$
As an example, if we consider the Nakajima–Zwanzig Master Equation,...
- 756
2
votes
1
answer
126
views
Antifields in BV formalism - do they also have gauge transformation laws?
I am studying Weinberg Vol 2 and the BV formalism of the gauge theory.
There, the antifields are introduced somewhat out of thin air. I am a little bit confused about their properties.
For example, ...
- 1,669
0
votes
1
answer
224
views
What is the Mathematical description of Weak Interaction at low energies?
Introduction
When I started to study gauge theory the mathematical road map seemed to be quite "simple". After all the concepts and notions about principal the differential geometry of fibre ...
- 3,085
4
votes
1
answer
310
views
Equivalence of Maxwell and electric field operator in the Coulomb gauge (minimal and polar coupling)
In the field theory literature, we find the interaction Hamiltonian coupling a point particle with charge $e$ and mass $m$ to the electromagnetic field to be
$$
\hat{H}_\text{int}(t)
=
-
\frac{e}{m}
\...
- 543
0
votes
1
answer
435
views
Fix temporal gauge $A_0=f$ using an appropriate gauge transformation
Consider the Lagrangian
\begin{equation}
\mathcal{L}= -\frac{1}{4} F_{\mu \nu}F^{\mu \nu} - A_{\mu}J^{\mu} \ \ \ \ \text{ with } \ \ \ \ F_{\mu \nu}=\partial_\mu A_\nu - \partial_{\nu}A_{\mu}.
\...
- 313
2
votes
1
answer
808
views
Mass terms for scalar lagrangians?
First off, a pre-question: if I got this wrong, then probably the whole reasoning is wrong as well.
Studying the lagrangian for a two-particle scalar field with a quartic interaction in the context of ...
- 5,931
2
votes
1
answer
83
views
Open gauge algebras apart from supergravity theories
Does anyone know of a gauge system that is not a model of (super-)gravity where the gauge algebra fails to close off-shell?
- 3,915
4
votes
2
answers
598
views
Gauge fixing, Lorentz invariance and positive definite metric of Hilbert space
Updated 0n ${\bf 02.04.2020}$
$\large{\bf Context}$
In the first $3$ minutes of this video lecture (based on the presentation here) on the subject matter of Goldstone theorem without Lorentz ...
- 26.8k
4
votes
1
answer
761
views
Parity Invariance Complex Scalar Field Lagrangian
I am trying to prove the parity invariance of some terms in a complex scalar field Lagrangian, for example $m^2 \; \phi^* \phi$ or $\partial_{\mu} \phi \;\partial^{\mu} \phi^*$. So what I want to ...
- 900
6
votes
0
answers
180
views
Stueckelberg mechanism in path integrals
Suppose we have some gauge invariant Lagrangian $\mathcal{L}_0$ depending on $A$ and some matter fields $\psi$, and we add a mass term for $A$.
$$\mathcal{L}[A,\psi]=\mathcal{L}_0[A,\psi]+m^2A^2$$
...
- 8,815